Question

Solve for the predicted values of y and the residuals for the following data.

x	12	21	28	8	20
y	17	15	22	19	24

Do not round the intermediate values. (Round your answers to 3 decimal places.)

x	y	Predicted (ŷ)	Residuals (y-ŷ)
12	17
21	15
28	22
8	19
20	24

Answer 1

The following data are passed:

X	Y
12	17
21	15
28	22
8	19
20	24

The independent variable is X, and the dependent variable is Y. In order to compute the regression coefficients, the following table needs to be used:

	X	Y	X*Y	X2	Y2
	12	17	204	144	289
	21	15	315	441	225
	28	22	616	784	484
	8	19	152	64	361
	20	24	480	400	576
Sum =	89	97	1767	1833	1935

Based on the above table, the following is calculated:

Therefore, based on the above calculations, the regression coefficients (the slope m, and the y-intercept n) are obtained as follows

Therefore, we find that the regression equation is:

Y = 16.5096 + 0.1624 X

x	y	Predicted (ŷ)	Residuals (y-ŷ)
12	17	18.4584	-1.4584
21	15	19.92	-4.92
28	22	21.0568	0.9432
8	19	17.8088	1.1912
20	24	19.7576	4.2424